During a position change or exchange of transport containers, the lowering rail and the pivoting rail in a carton filling machine of this type are removed from the container in unison by means of a connecting linkage and are then moved back into the transport container. As the lowering and pivoting rails are moved back into the transport container it is important that the downwardly projecting lowering rail opposite the pivoting rail be held as precisely as possible but with a predetermined space from the floor of the transport container or a previously loaded layer of blanks so as to avoid hinderance to the lowering rail during loading due to something such as protruding floor flaps of the carton.